If a triangle with a perimeter of 18 cm is divided by the median into 2 triangles with perimeters of 14

If a triangle with a perimeter of 18 cm is divided by the median into 2 triangles with perimeters of 14 and 16, then the length of the median is?

The perimeter of a triangle is the sum of the lengths of all sides of the triangle.

Let the length of one side be x cm, the second side y cm, and the third, to which the median is drawn, equal (2 * a) cm. For convenience of calculations, the length of the median will be considered equal to c cm.

Hence, the perimeter of this large triangle and the perimeter of the two small triangles:

{x + y + 2a = 18;

{x + a + c = 14;

{y + a + c = 16.

Received three equations with three unknowns, find the unknown with.

To do this, we find the sum of the second and third equations, and rewrite the first equation:

{x + y + 2a + 2c = 30;

{x + y + 2a = 18.

Substitute the value x + y + 2a:

18 + 2s = 30;

2s = 30 – 18;

2c = 12;

s = 6 (cm).

Answer: The median length is 6 cm.